Parameter Estimation Of The Load Sharing Parallel System

In reliability theory research and engineering practice,various redundancy technologies are usually used to improve the reliability of the system.The load sharing system is an extension of the redundant system,which means that when the components in the system fail,the total load of the system has to be redistributed to other surviving components,causing the load of the remaining components to increase and the failure rate to increase.Therefore,the risk of component failure increases.In real life,for the research of load sharing systems,only data is usually faced,but the distribution function lurking in the data is unknown,and then the distribution function needs to be estimated from the data through some methods.Kumaraswamy distribution and Exponential Pareto distribution are very useful in terms of reliability as life models.They are widely used in residents’ income distribution and many reliability projects,but their research on load sharing systems has been neglected.This paper mainly studies the point estimation and interval estimation of the parameters for the load sharing parallel system under these two distributions.The point estimates and confidence intervals of the parameters are obtained through simulation,and examples are introduced to study and analyze the method in the paper,and with the help of random order,the two distributions and the exponential distribution were randomly compared.First,for a load-sharing parallel system model,assuming that its component life is subject to Kumaraswamy distribution and Exponential Pareto distribution,respectively,its parameters are estimated by the maximum likelihood estimation method,and based on the theoretical properties of the asymptotic distribution for maximum likelihood estimation(MLE),the best asymptotically unbiased estimation(BAUE)of the model is obtained.In order to intuitively reflect the relationship between the parameters,this paper simulates the confidence ellipse between the parameters by computer,and combines the charts to analyze the estimated parameters.Secondly,in order to expand the sample size and improve the accuracy of estimation,this paper uses Bootstrap sampling technique to estimate the interval of the above two distributions,and obtains the Bootstrap point estimates and two confidence intervals.It can be seen from the simulation results that as the sample size increases,the accuracy of parameter estimation becomes higher and higher.Finally,this paper analyzes the point estimates and confidence intervals of the parameters by using actual data under exponential distribution and exponential Pareto distribution,which fully illustrates the practicability of the method used in this article.Andrandom order is used to compare the exponential distribution,Kumaraswamy distribution and Exponential Pareto distribution randomly.